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The formula to calculate the maturity amount is as follows: Total sum deposited+Interest on it = + = [+ (+)]. Banks in India use the following formula for recurring deposit (RD) maturity value: (Maturity value of RD; based on quarterly compounding): .
Expression (3) which uses the bond's yield to maturity to calculate discount factors. The key difference between the two durations is that the Fisher–Weil duration allows for the possibility of a sloping yield curve, whereas the second form is based on a constant value of the yield y {\displaystyle y} , not varying by term to payment. [ 10 ]
Present value calculations, and similarly future value calculations, are used to value loans, mortgages, annuities, sinking funds, perpetuities, bonds, and more. These calculations are used to make comparisons between cash flows that don’t occur at simultaneous times, [ 1 ] since time and dates must be consistent in order to make comparisons ...
The day count is also used to quantify periods of time when discounting a cash-flow to its present value. When a security such as a bond is sold between interest payment dates, the seller is eligible to some fraction of the coupon amount. The day count convention is used in many other formulas in financial mathematics as well.
WAL should not be confused with the following distinct concepts: Bond duration Bond duration is the weighted-average time to receive the discounted present values of all the cash flows (including both principal and interest), while WAL is the weighted-average time to receive simply the principal payments (not including interest, and not discounting).
The present value formula is the core formula for the time value of money; each of the other formulas is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations. The present value (PV) formula has four variables, each of which can be solved for by numerical methods:
where is the maturity of the longest transaction in the portfolio, is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity , is the loss given default, is the time of default, () is the exposure at time , and (,) is the risk neutral probability of counterparty default between times and .
Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below: